RE: "Apple may well diagnosis the issue for you, however refuse to service it—"
I'm pretty sure that Apple will refuse to service it.
The last 17-inch MacBook Pro came out in October 2011 – so that model is over 11 and 1/2 years old now. Others are even older. Apple considers hardware "obsolete" at the 7-year mark, and in many cases stops carrying repair parts and offering repair service at the 5-year "vintage" mark.
I believe the hard drive and battery are accessible on those old 17-inch MBPs. If the problem is that the HDD has died, the OP may be able to replace it with a new HDD or even a SSD (if he has a way to reload Mac OS X). If it is that the battery has given up the ghost, and he can find a compatible replacement battery for such an old Mac, that too, might be something he or a third-party repair shop could fix without needing a lot of assistance from Apple.
I don't know if those MBPs had clock batteries (separate from the main, rechargeable batteries). If they did, the possibility of a dead clock battery might be something to investigate.